Maximum number of ODLS in Brown's diagonal Latin squares of order N=2n, https://oeis.org/Axxxxxx

n=2, a(2)=0
Announcement: https://vk.com/wall162891802_2895, Eduard I. Vatutin, Dec 16 2024
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n=4, a(4)=1
Announcement: https://vk.com/wall162891802_2895, Eduard I. Vatutin, Dec 16 2024
Way of finding: brute force
0 1 2 3 
2 3 0 1 
3 2 1 0 
1 0 3 2 

n=6, a(6)=0
Announcement: https://vk.com/wall162891802_2895, Eduard I. Vatutin, Dec 16 2024
Way of finding: brute force
0 1 2 3 4 5 
1 2 0 5 3 4 
4 3 5 0 2 1 
3 0 1 4 5 2 
5 4 3 2 1 0 
2 5 4 1 0 3 

n=8, a(8)=824
Announcement: https://vk.com/wall162891802_2895, Eduard I. Vatutin, Dec 16 2024
Way of finding: brute force
0 1 2 3 4 5 6 7 
2 3 0 1 6 7 4 5 
4 5 6 7 0 1 2 3 
6 7 4 5 2 3 0 1 
3 2 1 0 7 6 5 4 
1 0 3 2 5 4 7 6 
7 6 5 4 3 2 1 0 
5 4 7 6 1 0 3 2 

n=10, a(10)=8
Announcement: -, Alexey D. Belyshev, Apr 27 2017
Way of finding: brute force
0 1 2 3 4 5 6 7 8 9 
1 2 3 4 0 9 5 6 7 8 
3 4 9 8 7 2 1 0 5 6 
8 7 6 5 9 0 4 3 2 1 
7 3 4 0 8 1 9 5 6 2 
5 0 8 7 3 6 2 1 9 4 
4 9 1 2 6 3 7 8 0 5 
2 6 5 9 1 8 0 4 3 7 
9 8 7 6 5 4 3 2 1 0 
6 5 0 1 2 7 8 9 4 3 

n=12, a(12)>=1764493860
Announcement: https://vk.com/wall162891802_1734, Eduard I. Vatutin, Aug 26 2021
0 1 2 3 4 5 6 7 8 9 10 11 
1 2 3 4 5 0 11 6 7 8 9 10 
5 0 1 2 3 4 7 8 9 10 11 6 
8 7 6 11 10 9 2 1 0 5 4 3 
7 6 11 10 9 8 3 2 1 0 5 4 
9 8 7 6 11 10 1 0 5 4 3 2 
6 11 10 9 8 7 4 3 2 1 0 5 
10 9 8 7 6 11 0 5 4 3 2 1 
11 10 9 8 7 6 5 4 3 2 1 0 
2 3 4 5 0 1 10 11 6 7 8 9 
4 5 0 1 2 3 8 9 10 11 6 7 
3 4 5 0 1 2 9 10 11 6 7 8 

Dec 22 2024